For a majority of the series, the name of the school was never said. In "Out of the Picture", Liam reveals that the name of the school is Royal Woods Elementary.
It is unknown if this is the only school in all Royal Woods, or if there are more schools.
However in the episode "Study Muffin", Clyde said that if Lincoln failed 5th grade, he'd have to go to middle school without him, implying that the school only goes up to 5th grade, and there are other schools in Royal Woods.
This school is most likely an elementary school fused with kindergarten.
So far the Louds that have been seen at the school are Lincoln, Lucy, Lana, Lola, and Lisa.
So far only classrooms and classmates of Lincoln and Lisa were shown.
For some reason, the flag is not moving, and has fewer stars and stripes.
During the school's first few appearances, the front of the school wasn't shown.